John has utility function U = C^0.4H^0.4for good C and housing H (housing measured in square feet). John's preferences are such that he always prefers more housing H (i.e., the larger the home or apartment in square-feet, H, the better); other than the size of the housing, all homes are identical quality, etc. (only differ in size).

John has income Y = $6,000.Market prices are PC= $1 per unit and PH= $3 per unit (square foot). Marginal utilities for C and H are:

MUC= 0.4C^-0.6H^0.4and MUH= 0.4C^0.4H^-0.6

a.Find the utility maximizing amounts of C and housing H (square feet).Show this graphically with H on the horizontal axis and C on the vertical axis.

b.John is eligible for a government assistance program that provides him a house of size H = 600 (i.e., 600 square foot home) for no cost.In other words, John can choose to live in the government housing of H = 600 for free, or he can pay $3 per unit H himself if he desires to live in a home smaller or larger than 600.Show how this program impacts his income constraint available for C and H.

c.Assume John still spends his entire income on C and H.Would John prefer to live in the free government house (H = 600) or would he choose to live in another home size H like you found in part a) and pay for it himself? Compare the utility levels in each case and illustrate graphically.